1. Field of the Invention
The present invention is directed to the directional attachment of an actuator/sensor to a substrate. More specifically, the present invention is directed to the directional attachment of an actuator/sensor to a substrate such that it is possible to actuate/sense strains in the substrate in a desired direction, regardless of the passive stiffness properties of the substrate, actuator element, or sensor element.
2. Discussion of Background
Currently, a structure can only be actuated by a piezoelectric, magnetostrictive, thermally actuated lamina (including bi-metallic) or shape memory alloy (SMA) elements isotropically, which means that a twist or torsional deflection can be produced in the structure if and only if it is fully attached and extension-twist or bending-twist coupled. The same holds true for sensing; currently, a structure must be fully attached and extension-twist coupled or bending-twist coupled to piezoelectric, magnetostrictive, thermally actuated lamina (including bi-metallic) or shape memory alloy (SMA) sensors aligned to sense the twist through the amount of extension or bending. FIG. 7 shows two fully attached actuator/sensor elements 10 attached to a substrate 30 in a bending-twist coupled arrangement. FIG. 8 shows two fully attached actuator/sensor elements 10 attached to a substrate 30 in an extension twist coupled arrangement. Thus, these arrangements do not allow twist or torsional deflections in a substrate to be actuated or sensed regardless of the passive structural properties of the substrate.
Coupling actuator/sensor elements to structures has been shown to be particularly useful in controlling and reducing vibration in several types of aeronautical and aerospace structures. Applications include vibration suppression in space trusses, dynamic control of camber and twist for gust alleviation and flutter suppression on fixed wing surfaces. Vibration suppression in rotorcraft could also be enhanced through the use of intelligent actuators because current methods of vibration reduction in rotorcraft or helicopters do not address some of the vibration inducing phenomena that occur in actual helicopters including differences in individual blade tracking and magnitude and locations of dynamic stall. Because the unsteady bending moments in a rotor blade are several orders of magnitude greater than present intelligent actuators can impart, direct manipulation of the rotor blade and bending is currently not feasible. However, through blade twist manipulation many types of vibration reduction methods can be employed including suppression of blade vibrational modes, in flight tracking and dynamic stall reduction through small amplitude pitch oscillation, as well as higher harmonic control (HHC) and individual blade control (IBC).
Implementation of dynamic blade twist requires the introduction of torsional forcing to orthotropic or quasi-orthotropic blade structures such as uncoupled composite or aluminum blades. Since nearly all composite rotor blades in use today have such characteristics, a method of torsional forcing must be developed. Many types of intelligent actuation devices, including piezoelectric actuators, in production today are incapable of imparting this torsional forcing due to their quasi-isotropic nature. Therefore, these systems do not allow the coupling of actuators/sensors to rotor blades in such a way that the behavior of the actuators/sensors is anisotropic.
Through classical laminated plate theory, the principles of directional attachment can be examined. Assuming the actuator/sensor is isotropic or quasiisotropic, as most suitable actuator/sensor materials are, it is not possible to directly actuate or sense strains that arise from torsional deformations. For an isotropic material, the longitudinal modulus, E.sub.L, the transverse modulus, E.sub.T, and the Poisson's ratios, .upsilon..sub.LT, .upsilon..sub.TL, are equal. Utilizing the mathematical analysis given in "Mechanics of Composite Materials", Jones, R. M., published by Hemisphere Publishing Company, New York, N.Y., 1975, the reduced stiffnesses (in tensor notation) as given by equation 2.61 in Jones, 1975, are as follows: ##EQU1## E*.sub.1111 =reduced stiffness in longitudinal direction (GPA, MSI) E*.sub.2222 =reduced stiffness in transverse direction (GPA, MSI)
E*.sub.1122 =reduced coupling stiffness (GPA, MSI) PA1 E*.sub.1212 =shear modulus (GPA, MSI) PA1 .epsilon..degree..sub.12 =shear strain (M/M, IN/IN) PA1 .kappa..degree..sub.11 =longitudinal bending (RAD/M) PA1 .kappa..degree..sub.22 =transverse bending (RAD/M) PA1 .kappa..degree..sub.12 =twist (RAD/M) PA1 E.sub.3 =charge across crystal in thickness direction (V) PA1 d.sub.31 =transverse charge coefficient (.mu. strain/.sub.(V/mm)) PA1 d.sub.33 =direct charge coefficient (.mu. strain/.sub.(V/mm)) PA1 d.sub.15 =shear coupling charge (.mu. strain/.sub.(V/mm)) PA1 V.sub.3 =potential across crystal in thickness direction PA1 g.sub.31 =transverse voltage coefficient PA1 g.sub.33 =direct voltage coefficient PA1 g.sub.15 =shear coupling voltage
For isotropic actuator/sensor elements, from equations 1, E*.sub.1111 =E*.sub.2222. If the actuator/sensor element is rotated to a particular angle with respect to the laminate or substrate, the rotated reduced stiffnesses are given by equations 2.80, Jones 1975, as follows: EQU E.sub.1111 =E*.sub.1111 Cos.sup.4 .theta.+2(E*.sub.1122 +2E*.sub.1212) Sin.sup.2 .theta.Cos.sup.2 .theta.+E*.sub.2222 Sin.sup.4 .theta. EQU E*.sub.2222 =E*.sub.1111 Sin.sup.4 .theta.2(E*.sub.1122 +2E*.sub.1212) Sin.sup.2 .theta.Cos.sup.2 .theta.+E*.sub.2222 Cos.sup.4 .theta. EQU E.sub.1122 =(E*.sub.1111 +E*.sub.2222 -4E*.sub.1212) Sin.sup.2 .theta.Cos.sup.2 .theta.+E*.sub.1122 (Sin .sup.4 .theta.+Cos.sup.4 .theta.) EQU E.sub.1212 =(E*.sub.1111 +E*.sub.2222 -E*.sub.1122 -2E*.sub.1212) Sin.sup.2 +Cos.sup.2 .theta.E*.sub.1212 (Sin.sup.4 .theta.+Cos.sup.4 .theta.) EQU E.sub.1112 =(E*.sub.1111 -E*.sub.1122 -2E*.sub.1212) Sin .theta.Cos.sup.3 .theta.+(E*.sub.1122 -E*.sub.2222 +2E*.sub.1212) Sin.sup.3 .theta.Cos .theta. EQU E.sub.2212 =(E*.sub.1111 -E*.sub.1122 -2E*.sub.1212) Sin.sup.3 .theta.Cos .theta.+(E*.sub.1122 -E*.sub.2222 2E*.sub.1212) Sin .theta.Cos.sup.3 .theta. (2)
From equations 2, for an isotropic actuator/sensor element, it is seen that the rotated reduced stiffnesses are the same as the non-rotated stiffnesses and E*.sub.1112 =E*2212=0. Accordingly, the rotation angle has no effect on an actuator/sensor material that is completely integrated into or attached to a substrate. The strain energy in a beam demonstrates the relationship between the passive structure or substrate (laminate, 1am.) and the actuator/sensor (a/s) as follows: ##EQU2## .epsilon..degree..sub.11 =longitudinal extension strain (M/M, IN/IN) .epsilon..degree..sub.22 =transverse extension strain (M/M, IN/IN)
N=number of plys, k=individual ply, z=distance through the thickness, as given in Jones, 1975.
For piezoelectric crystals, the strain actuation matrix is composed of actuation voltages, E.sub.x, and charge coefficients, d.sub.xx, and according to equation 29 from a paper titled "Development of Piezoelectric Technology for Applications in Control of Intelligent Structures" by Crawley, E. F. et al. presented at the American Control Conference, June 1988, are related to the actuation strain matrix by, ##EQU3## E.sub.1 =charge across crystal in longitudinal direction (V) E.sub.2 =charge across crystal in transverse direction (V)
Similarly, for a piezoelectric sensor, the strain sensing matrix is composed of sensing voltages, V.sub.x, and voltage coefficients, g.sub.xx. ##EQU4## V.sub.1 =potential across crystal in longitudinal direction V.sub.2 =potential across crystal in transverse direction
For practical purposes, the only voltages that can be actuated or sensed are through the thickness of the actuator/sensor element (E.sub.3 d.sub.31, V.sub.3 g.sub.31) because of the lead attachment area, equations 6 and 7 follow: EQU [.epsilon..sup.0.sub.11 .epsilon..sup.0.sub.22 .epsilon..sup.0.sub.12 .kappa..sub.11 .kappa..sub.22 .kappa..sub.12 ].sub.s =[E.sub.3 d.sub.31 E.sub.3 d.sub.31 0 0 0 0] (6) EQU [.epsilon..sup.0.sub.11 .epsilon..sup.0.sub.22 .epsilon..sup.0.sub.12 .kappa..sub.11 .kappa..sub.22 .kappa..sub.12 ].sub.s =[V.sub.3 g.sub.31 V.sub.3 g.sub.31 0 0 0 0] (7)
From equations 1 through 7, the only types of actuation/sensing that current (isotropic) types of fully attached actuator/sensor elements can actuate/sense are longitudinal extension, .epsilon..sup.0.sub.11, lateral extension, .epsilon..sup.0.sub.22 longitudinal bending, .kappa..sub.11, and lateral bending .kappa..sub.22. For the fully attached, isotropic actuator/sensor, .epsilon..sup.0.sub.11 cannot be distinguished from .epsilon..sup.0.sub.22, and .kappa..sub.11 cannot be distinguished from The shear strain, .epsilon..sup.0.sub.12 and the twist, .kappa..sub.12, cannot be actuated or sensed at all.